# How do you simplify (9sqrt2)/sqrt(6)?

Jul 1, 2016

$3 \sqrt{3}$

#### Explanation:

First we recognize that $6 = 2 \cdot 3$
That allows us to write $\sqrt{6}$ as $\sqrt{2 \cdot 3}$
Square roots of multiplications can be split so $\sqrt{2 \cdot 3} = \sqrt{2} \cdot \sqrt{3}$
So,$\frac{9 \sqrt{2}}{\sqrt{2} \cdot \sqrt{3}}$
That will allow us to eliminate the $\sqrt{2}$ from the top and bottom leaving us with $\frac{9}{\sqrt{3}}$
Now we split 9 into $3 \cdot 3$ and further split one of those 3s into $\sqrt{3} \cdot \sqrt{3}$
leaving: $\frac{3 \cdot \sqrt{3} \cdot \sqrt{3}}{\sqrt{3}}$
Eliminate one of the $\sqrt{3}$ from the top and the one from the bottom leaving us with the final answer of:
$3 \sqrt{3}$